Euler's forumula

It is a pretty cool thing:

One professor of mine made a pretty bold claim the other day about it. He said that any trig identity can be derived using this and only this formula. So here's an idea. Take a trig identity and see if you can prove it using nothing else. If you can, post it here. Any identity that we can prove using only Euler's Formula is fair game (i.e. you can use it in another proof), but you gotta prove it first before you can use it.

If you run into one that you have trouble with, by all means, post it.

I'm a bit short on time, so I'll post one up later tonight.

Edit:

Whoops, thanks mathsyperson

Last edited by Ricky (2006-03-19 04:24:09)

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

Re: Euler's forumula

George, I agree. And actually, I agreed before you ever backed up your statement. I really just wanted you to start showing what you said instead of just stating it.

But I think you missed the entire point of this topic. There is only one trig formula, and if you accept this formula, then you can generate every single other trig identity.

We aren't proving things. Now I have used the word prove before, but what I meant was "assuming that e^iθ = cosθ + isinθ, prove that ...." Sorry if the wording I used was bad, I should have used "show" instead of "prove."

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."